Answer:
Hello your question is incomplete attached below is the complete question
Answer : x ( acceleration of mass 4m ) = 
The top pulley rotates because it has to keep the center of mass of the system at equilibrium
Explanation:
Given data:
mass suspended = 4 meters
mass suspended at other end = 3 meters
first we have to express the kinetic and potential energy equations
The general kinetic energy of the system can be written as
T = 
T = 
also the general potential energy can be expressed as
U = 
The Lagrangian of the problem can now be setup as
next we will take the Euler-Lagrange equation for the generalized equations :
Euler-Lagrange equation = 
solving the equations simultaneously
x ( acceleration of mass 4m ) =
The top pulley rotates because it has to keep the center of mass of the system at equilibrium
To solve this problem we will start from the definition of energy of a spring mass system based on the simple harmonic movement. Using the relationship of equality and balance between both systems we will find the relationship of the amplitudes in terms of angular velocities. Using the equivalent expressions of angular velocity we will find the final ratio. This is,
The energy of the system having mass m is,
The energy of the system having mass 2m is,
For the two expressions mentioned above remember that the variables mean
m = mass
Angular velocity
A = Amplitude
The energies of the two system are same then,
Remember that
Replacing this value we have then
But the value of the mass was previously given, then
Therefore the ratio of the oscillation amplitudes it is the same.
This question is incomplete, the complete question is;
The Figure shows a container that is sealed at the top by a moveable piston, Inside the container is an ideal gas at 1.00 atm. 20.0°C and 1.00 L.
"What will the pressure inside the container become if the piston is moved to the 1.60 L mark while the temperature of the gas is kept constant?"
Answer:
the pressure inside the container become 0.625 atm if the piston is moved to the 1.60 L mark while the temperature of the gas is kept constant
Explanation:
Given that;
P₁ = 1.00 atm
P₂ = ?
V₁ = 1 L
V₂ = 1.60 L
the temperature of the gas is kept constant
we know that;
P₁V₁ = P₂V₂
so we substitute
1 × 1 = P₂ × 1.60
P₂ = 1 / 1.60
P₂ = 0.625 atm
Therefore the pressure inside the container become 0.625 atm if the piston is moved to the 1.60 L mark while the temperature of the gas is kept constant
Given that,
Mass of each washer = 4.9 g
We need to calculate the mass of two washers in kg
Using conversion of unit
Mass of each washer 
So, Mass of two washers is
Put the value of m
If 4 washer are attached to the spring
We need to calculate the applied force on the car
Using formula of force
Put the value into the formula
Hence, (i), The mass of two washers is 0.0098 kg.
(ii). The applied force on the car is 0.192 N.
The car would go from zero to 58.0 mph in 2.6 sec.
Since the force on the car is constant, therefore the acceleration of the car would also be constant.
Now for constant acceleration we can use the equation of motion
Using first equation of motion to calculate the acceleration of the car
v=u+at
29=0+a×1.30 ...... Eq. (1)
Again using the first equation of motion
58=0+a*t ....... Eq. (2)
Dividing eq. (2) with equation 1
t=2×1.3
t=2.6 sec
